Can the ability of Golden Guardian be activated at any time? Say, during another player's turn or during an attacker's or blockers fast effects phase?
Yes, activated abilities can by activated at any time you have priority, unless the ability states otherwise, which is not the case with Golden Guardian. This is per Comprehensive Rules:
112.3b Activated abilities have a cost and an effect. They are written as “[Cost]: [Effect.] [Activation instructions (if any).]” A player may activate such an ability whenever they have priority. (...)